Persistent, Niggling Questions

[Zeke]

Lexy! Good to see you. Stay a while.

[Alexia]

You may find me lurking :P It's either that, or do some work...

[Nate the Great]

In listening to the Tom Lehrer song "New Math", I started wondering...

PNQ: Aside from base-10 and base-2, are any other bases actually used by anyone.

I mean of the bases from 2 through 10. Sure, sometimes we use something akin to base-12, but only in an abstract sense. Schoolhouse Rock proposed two new symbols (dek and el) to represent "ten" and "eleven" in a base-12 counting system, but we'd never use them to convert Imperial units or traditional British currency.

So yeah, what point was there in teaching other bases to kids? Even the base-2 calculations we have to do seldom require pencil and paper, we use base-2 for the benefit of the computers, not ourselves.

[Zeke]

Hex! Programmers use hexadecimal all the time. Its usefulness stems from the fact that it's basically shorthand for binary.

Teaching arbitrary bases is important, just nowhere near as important as the New Math tried to make it. (Same goes for set theory.) Historically, not every civilization has used base ten. The Babylonians used base 60, the Mayans base 20, and so on. It's good to have some introduction to the concept.

[Nate the Great]

Yeah, but there's absolutely no reason to attempt teaching other bases to children before high school.

[Zeke]

I might hold out for junior high, but we basically agree. And it was even sillier at the time New Math was actually developed -- computers were nowhere near as important as they are today, and programming is really the only field where knowing other bases is of practical importance. (Yes, this means that before computers came along, other bases were just a curiosity. That's still true of all bases except 2, thanks to one of the great insights of the last century: if you can represent everything with 1s and 0s, you can do it with open and closed circuits.)

That said, I love mathematical curiosities. There's quality time to be spent at Wikipedia looking up different bases and their obscure applications. Did you know a couple of cultures have used base 8 because they counted by spaces between fingers, not by fingers themselves?

[NAHTMMM]

Originally Posted by Zeke

Did you know a couple of cultures have used base 8 because they counted by spaces between fingers, not by fingers themselves?

That I did not.